We explore a possibility for the Universe to cross $w=\ensuremath{-}1$ cosmological constant barrier dark energy state parameter. consider as slowly decaying D3-brane. The D3-brane dynamics are approximately described by nonlocal string tachyon interaction and backreaction of gravity is incorporated in closed dynamics. In local effective approximation this model contains one phantom component usual field with simple polynomial interaction. To understand properties system we study toy models...

One of the greatest problems primordial inflation is that inflationary space-time past-incomplete. This mainly because Einstein's GR suffers from a space-like Big Bang singularity. It has recently been shown ghost-free, non-local higher-derivative ultra-violet modifications gravity may be able to resolve cosmological singularity via non-singular bounce. Within framework such models, we are going study both sub- and super-Hubble perturbations around an trajectory which preceded by Bounce in...

In this paper we study the most general covariant action of gravity up to terms that are quadratic in curvature. particular includes non-local, infinite derivative theories which ghost-free and exhibit asymptotic freedom ultraviolet. We provide a detailed algorithm for deriving equations motion such actions containing an arbitrary number D'Alembertian operators, is our main result. also perform tests on field derive, including checking Bianchi identities weak-field limit. Lastly, consider...

In this paper we show that there is a universal prediction for the Newtonian potential an infinite derivative, ghost-free, quadratic curvature gravity. We in order to make such theory ghost-free at perturbative level, always falls-off as 1/r infrared limit, while short distances becomes non-singular. provide examples which can potentially test scale of gravitational non-locality up 0.004 eV.

In this paper we provide the criteria for any generally covariant, parity preserving, and torsion-free theory of gravity to possess a stable de Sitter (dS) or anti--de (AdS) background. By stability mean absence tachyonic ghostlike states in perturbative spectrum that can lead classical instabilities violation quantum unitarity. While find usual suspects, $F(R)$ $F(G)$ theories, indeed consistent (A)dS backgrounds, $G$ being Gauss-Bonnet term, another interesting class string-inspired...

In this paper we will show all the linearized curvature tensors in infinite derivative ghost and singularity free theory of gravity static limit. We have found that region non-locality, ultraviolet regime (at short distance from source), Ricci tensor scalar are not vanishing, meaning do a vacuum solution anymore due to smearing source induced by presence non-local gravitational interactions. It also follows that, unlike Einstein's gravity, Riemann is traceless it does coincide with Weyl...

It is natural to expect a consistent inflationary model of the very early Universe be an effective theory quantum gravity, at least energies much less than Planck one. For moment, $R+R^2$, or shortly $R^2$, inflation most successful in accounting for latest CMB data from PLANCK satellite and other experiments. Moreover, recently it was shown ultra-violet (UV) complete via embedding into analytic infinite derivative (AID) non-local gravity. In this paper, we derive general gravity that...

The $R+R^2$, shortly named "$R^2$" ("Starobinsky") inflationary model, represents a fully consistent example of one-parameter scenario. This model has "graceful exit" from inflation and provides mechanism for subsequent creation final thermalization the standard matter. Moreover, it produces very good fit observed spectrum primordial perturbations. In present paper we show explicitly that $R^2$ spacetime is an exact solution range weakly non-local (quasi-polynomial) gravitational theories,...

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well field theories string theories. We consider quantum emphasizing an issue of their renormalizability the UV/IR mixing. Sen's conjectures on open tachyon condensation application to D-brane physics have led wide investigations covariant theory proposed by Witten about 15 years ago. review main ingredients cubic (super)string using various formulations: functional, operator, conformal...

In Einstein's theory of general relativity the vacuum solution yields a blackhole with curvature singularity, where there exists point-like source Dirac delta distribution which is introduced as boundary condition in static case. It has been known for while that ghost-free infinite derivative gravity can ameliorate such singularity at least level linear perturbation around Minkowski background. this paper, we will show Schwarzschild metric does not satisfy origin within gravity, since...

Einstein's general theory of relativity is plagued by cosmological and black-hole type singularities Recently, it has been shown that infinite derivative, ghost free, gravity can yield nonsingular mini-black hole solutions. In particular, the possesses a mass-gap determined scale new physics. This paper provides plausible argument, not no-go theorem, based on Area-law gravitational entropy within compact objects in static limit need have horizons.

The vacuum solution of Einstein's theory general relativity provides a rotating metric with ring singularity, which is covered by the inner and outer horizons, an ergo region. In this paper, we will discuss how ghost-free, quadratic curvature, Infinite Derivative Gravity (IDG) may resolve singularity. IDG non-locality gravitational interaction can smear out delta-Dirac source distribution making potential finite everywhere including at $r=0$. We show that same feature also holds for metric....

A bstract In this paper we will study R 2 -like inflation in a non-local modification of gravity which contains quadratic Ricci scalar and Weyl tensor terms with analytic infinite derivative form-factors the action. It is known that inflationary solution local + remains particular exact model. was shown earlier power spectrum perturbations generated during setup same as inflation, whereas gets modified due to squared term. present go beyond 2-point correlators compute non-Gaussian parameter...

We consider the most general quadratic in curvature stringy motivated non-local action for modified Einstein's gravity. present exact analytic cosmological solutions including bouncing ones and develop relevant techniques further study of this type models. also elaborate on perturbation formalism argue that found solution is stable during bounce phase.

In this paper, we will study the complete equations of motion for a ghost-free quadratic-curvature infinite-derivative gravity. We argue that within scale nonlocality, Schwarzschild-type singular metric solution is not permissible. Therefore, vacuum which prediction in Einstein-Hilbert gravity may persist region nonlocality. also show just gravity, without infinite derivatives, always allows solution.

In this work we explicitly show that the perturbative unitarity of analytic infinite derivative scalar field theories can be achieved using a modified prescription for computing scattering amplitudes. The crux new is continuation result obtained in Euclidean signature to Minkowski external momenta. We intensively elaborate an example nonlocal ${\ensuremath{\phi}}^{4}$ model various operators. General UV properties amplitudes are discussed.

The $R^2$ inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion the early Universe governed Ricci being eigenmode d'Alembertian operator. In this paper, we derive most theory gravity admitting inflationary solution turned out to be higher non-local GR. We study in detail perturbations and analyse structure form-factors that leads massive (scalaron) massless tensor degrees freedom. argue contains only finite number free...